Haryana Police Constable Model Paper 3

We know that,
Volume of cube = ${\mathrm{a}}^3$ where, a = side of the cube
Volume of sphere = $\left(\frac{4}{3}\right)\mathrm{\pi }{\mathrm{r}}^3$ where, r = radius of the sphere
Let,
Side of the cube = a
Since, the sphere exactly fit inside the cube
∴ Radius of the sphere = r = $\frac{\mathrm{a}}{2}$
∴ Required ratio
$=\frac{{\mathrm{a}}^3}{\frac{4}{3}\times \mathrm{\pi }\times {\left(\frac{\mathrm{a}}{2}\right)}^3}=\frac{3\times 8\times {\mathrm{a}}^3}{4\times \mathrm{\pi }\times {\mathrm{a}}^3}=\frac{6}{\mathrm{\pi }}=6:\mathrm{\pi }$